System and method for maximising thermal efficiency of a power plant

ABSTRACT

A method for maximising thermal efficiency of a power plant, the method comprising obtaining the current state of the plant from available measured data; obtaining a set of Variables representing a current state of the power plant; applying a set of constraints to the Variables; generating a revised set of Variables representing a revised state of the power plant; and testing the revised set of Variables within a mathematical model for convergence. Generating the revised set of Variable is based at least partly on Euler&#39;s equation, the conservation of mass equation; and a mathematical description of a reversible continuum. There are also provided a related power plant thermal efficiency maximisation system and computer program.

CROSS-REFERENCE SECTION

This application claims the benefit of International Application No.PCT/NZ2010/000222, filed Nov. 8, 2010, and entitled “SYSTEM AND METHODFOR MAXIMISING THERMAL EFFICIENCY OF A POWER PLANT”, which claims thebenefit of U.S. Provisional Patent Application No. 61/259,516, filedNov. 9, 2009, and entitled “SYSTEM AND METHOD FOR MAXIMIZING THERMALEFFICIENCY OF A POWER PLANT,” which are hereby incorporated by referencein their entireties.

BACKGROUND

Experience shows that significant efficiency increase due to real timetuning of thermal power-plants is feasible. It would be helpful toprovide a system that systematically yields the absolute maximum ofthermal efficiency η of a plant with respect to a set of independentmeasured parameters. The parameters, also referred to as Variables, arepreferably available to an operator or an engineer to manipulate,subject to operational, safety, structural, and environmentalconstraints. The technique would ideally be applicable to any type ofenergy-conversion plant in particular thermal power plants. Thermalpower plants include, but are not restricted to steam-turbine, combinedcycle, co-generation power-plants, Diesel cycles, and nuclear.

It is an object of the invention to go some way toward maximisingthermal efficiency of a power plant, or to at least provide the publicwith a useful choice.

SUMMARY OF INVENTION

In one embodiment the invention comprises a method for maximisingthermal efficiency of a power plant, the method comprising:

-   -   obtaining the current state of the plant from available measured        data;    -   obtaining a set of Variables representing a current state of the        power plant;    -   applying a set of constraints to the Variables;    -   generating a revised set of Variables representing a revised        state of the power plant, the generation based at least partly        on:

Euler's equation

${{\rho \; \frac{\partial\overset{arrow}{v}}{\partial t}} = {{\frac{\partial( {\rho \; \overset{arrow}{v}} )}{\partial t} + {{\rho ( {\overset{arrow}{v} \cdot V} )}\overset{arrow}{v}}} = {{- {\nabla P}} - {\sum{{\overset{arrow}{F}}_{k} \cdot {{\overset{arrow}{j}}_{k}.}}}}}};$

and the conservation of mass equation

${{\frac{\partial( {A\; \rho_{k}} )}{\partial t} + {\nabla{\cdot \lbrack {A( {{\overset{arrow}{j}}_{k} + {\rho_{k}\overset{arrow}{v}}} )} \rbrack}}} = {\frac{\partial}{\partial t}\lbrack {A \times M_{k}{\sum\limits_{j = 1}^{r}{v_{kj}( {\rho \; {\overset{\sim}{n}}_{j}} )}}} \rbrack}};$

and

-   -   a mathematical description of a reversible continuum; and    -   testing the revised set of Variables within a mathematical model        for convergence.

Preferably the mathematical description of the reversible continuumcomprises:

-   -   the reversible conservation of energy equation

${{{\frac{\partial}{\partial t}( {{\rho \; \frac{1}{2}{\overset{arrow}{v}}^{2}} + \psi} )} + {\nabla{\cdot ( {{\rho \; \frac{1}{2}{\overset{arrow}{v}}^{2}} + \psi} )}} + ( {{\sum\limits_{f = 1}^{R}{\sum\limits_{k = 1}^{K}{\mu_{k}v_{kj}J_{j}}}} - {\rho \; \overset{.}{Q}}} )} = {- ( {{\sum{\mu_{k}\frac{{\partial\rho}\; c_{k}}{\partial t}}} + {{\nabla{\cdot {\rho ( {h - T_{g}} )}}}\overset{arrow}{v}} - {\nabla{\cdot {\sum{\mu_{k}{\overset{arrow}{j}}_{k}}}}}} )}};$

and

-   -   the thermodynamic equations of state

p=p(P,T,c _(k)),h−Ts=g=g(P,T,c _(k)),μ_(k)=μ_(k)(P,T,c _(k)),k=1 . . . N

Preferably the mathematical description of the reversible continuumcomprises the geodesic equations

${{{\frac{\partial{\overset{.}{R}}^{k}}{\partial R^{j}}{\overset{.}{R}}^{j}} + {\begin{Bmatrix}k \\{ij}\end{Bmatrix}{\overset{.}{R}}^{i}{\overset{.}{R}}^{j}}} = 0};{\frac{R^{k}}{t} = {{\overset{.}{R}}^{k}.}}$

Preferably the method further comprises repeating the steps ofgenerating the revised set of Variables and testing the revised set ofVariables within the mathematical model until each of the revised set ofVariables reaches a variance less than a threshold variance.

Preferably generating the revised set of variables is based at leastpartly on the equation

${\frac{1}{A}\frac{A}{x}} = {{\frac{1}{\rho \; u^{2}}\frac{P}{x}( {1 - {u^{2}\frac{\partial\rho}{\partial P}}} )} = {\frac{1}{\rho \; u^{2}}{\frac{P}{{x( {1 - {Ma}^{2}} )}}.}}}$

Preferably generating the revised set of variables is based at leastpartly on the equation

$\frac{\partial( {{A\; \rho_{k}u} + j_{k}} )}{\partial x} = {{\frac{\partial}{\partial t}\lbrack {A \times M_{k}{\sum\limits_{j = 1}^{r}{v_{kj}( {\rho \; {\overset{\sim}{n}}_{j}} )}}} \rbrack}.}$

Preferably generating the revised set of variables is based at leastpartly on the equation

${{\frac{\partial}{\partial x}( {{\rho \; \frac{1}{2}u^{2}} + \psi} )} + ( {{\sum\limits_{j = 1}^{R}{\sum\limits_{k = 1}^{K}{\mu_{k}v_{kj}J_{j}}}} - {\rho \; \overset{.}{Q}}} )} = {- \lbrack {\frac{\partial}{\partial x}( {{{\rho ( {h - T_{g}} )}u} - {\sum{\mu_{k}j_{k}}}} )} \rbrack}$

Preferably testing the revised set of variables for convergenceincludes:

-   -   calculating the kinetic energy of each reversible continuum of        the power plant at an initial state Aent;    -   calculating the kinetic energy of each reversible continuum of        the power plant at a subsequent state Aex; and    -   calculating the difference between the kinetic energy at Aex and        the kinetic energy at Aent.

Preferably testing the revised set of variables for convergence includesminimizing the sum of individual calculated differences between thekinetic energy at Aex and the kinetic energy at Aent.

Preferably one or more of the calculated differences is determined bythe normalized equation

$\mspace{20mu} {\text{?} = {{\sum{\int_{P{({- 1})}}^{P{(1)}}{\frac{1}{\rho}{P}}}} = {\int_{- 1}^{1}{A\; \rho \; u\; \frac{1}{2}u^{2}{x}}}}}$?indicates text missing or illegible when filed

In a further embodiment the invention comprises a computer readablemedium on which is stored computer executable instructions that whenexecuted by a processor cause the processor to perform any one of theabove methods.

In a further embodiment the invention comprises a power plant thermalefficiency maximisation system comprising:

-   -   a minimiser configured to apply a set of constraints to a set of        Variables, the Variables representing a current state of a power        plant;    -   a solver configured to generate a revised set of Variables        representing a revised state of the power plant, the generation        based at least partly on:

Euler's equation

${{\rho \; \frac{\partial\overset{arrow}{v}}{\partial t}} = {{\frac{\partial( {\rho \; \overset{arrow}{v}} )}{\partial t} + {{\rho ( {\overset{arrow}{v} \cdot V} )}\overset{arrow}{v}}} = {{- {VP}} - {\sum{{\overset{arrow}{F}}_{k} \cdot {{\overset{arrow}{j}}_{k}.}}}}}};$

and

-   -   the conservation of mass equation

${{\frac{\partial( {A\; \rho_{k}} )}{\partial t} + {V \cdot \lbrack {A( {{\overset{arrow}{j}}_{k} + {\rho_{k}\overset{arrow}{v}}} )} \rbrack}} = {\frac{\partial}{\partial t}\lbrack {A \times M_{k}{\sum\limits_{j = 1}^{r}{v_{kj}( {\rho \; {\overset{\sim}{n}}_{j}} )}}} \rbrack}};$

and

-   -   a mathematical description of a reversible continuum; and    -   a convergence tester configured to test the revised set of        Variables for convergence.

Preferably the mathematical description of the reversible continuumcomprises:

-   -   the reversible conservation of energy equation

${{\frac{\partial}{\partial t}( {{\rho \; \frac{1}{2}{\overset{arrow}{v}}^{2}} + \psi} )} + {\nabla{\cdot ( {{\rho \; \frac{1}{2}{\overset{arrow}{v}}^{2}} + \psi} )}} + ( {{\sum\limits_{j = 1}^{R}{\sum\limits_{k = 1}^{K}{\mu_{k}v_{kj}J_{j}}}} - {\rho \; \overset{.}{Q}}} )} = {- ( {{\sum\; {\mu_{k}\; \frac{{\partial\rho}\; c_{k}}{\partial t}}} + {{\nabla{\cdot {\rho ( {h - T_{g}} )}}}\overset{arrow}{v}} - {\nabla{\cdot {\sum{\mu_{k}{\overset{arrow}{j}}_{k}}}}}} )}$

and

-   -   the thermodynamic equations of state

p=p(P,T,c _(k)),h−Ts=g=g(P,T,c _(k)),μ_(k)=μ_(k)(P,T,c _(k)),k=1 . . . N

Preferably the mathematical description of the reversible continuumcomprises the geodesic equations

${{{\frac{\partial{\overset{.}{R}}^{k}}{\partial R^{j}}{\overset{.}{R}}^{j}} + {\begin{Bmatrix}k \\{ij}\end{Bmatrix}{\overset{.}{R}}^{i}{\overset{.}{R}}^{j}}} = 0};{\frac{R^{k}}{t} = {{\overset{.}{R}}^{k}.}}$

Preferably the solver is configured to repeat the steps of generatingthe revised set of Variables and testing the revised set of Variableswithin the mathematical model until each of the revised set of Variablesreaches a variance less than a threshold variance.

Preferably generating the revised set of variables is based at leastpartly on the equation

${\frac{1}{A}\frac{A}{x}} = {{\frac{1}{\rho \; u^{2}}\frac{P}{x}( {1 - {u^{2}\frac{\partial\rho}{\partial P}}} )} = {\frac{1}{\rho \; u^{2}}{\frac{P}{{x( {1 - {Ma}^{2}} )}}.}}}$

Preferably generating the revised set of variables is based at leastpartly on the equation

$\frac{\partial( {{A\; \rho_{k}u} + j_{k}} )}{\partial x} = {{\frac{\partial}{\partial t}\lbrack {A \times M_{k}{\sum\limits_{j = 1}^{r}{v_{kj}( {\rho \; {\overset{\sim}{n}}_{j}} )}}} \rbrack}.}$

Preferably generating the revised set of variables is based at leastpartly on the equation

${{\frac{\partial}{\partial x}( {{\rho \; \frac{1}{2}u^{2}} + \psi} )} + ( {{\sum\limits_{j = 1}^{R}{\sum\limits_{k = 1}^{K}{\mu_{k}v_{kj}J_{j}}}} - {\rho \; \overset{.}{Q}}} )} = {- \lbrack {\frac{\partial}{\partial x}( {{{\rho ( {h - T_{g}} )}u} - {\sum{\mu_{k}j_{k}}}} )} \rbrack}$

Preferably the convergence tester is configured to test the revised setof variables for convergence, including:

-   -   calculating the kinetic energy of each reversible continuum of        the power plant at an initial state Aent;    -   calculating the kinetic energy of each reversible continuum of        the power plant at a subsequent state Aex; and    -   calculating the difference between the kinetic energy at Aex and        the kinetic energy at Aent.

Preferably testing the revised set of variables for convergence includesminimizing the sum of individual calculated differences between thekinetic energy at Aex and the kinetic energy at Aent.

Preferably one or more of the calculated differences is determined bythe normalized equation

$\mspace{20mu} {\text{?} = {{\sum{\int_{P{({- 1})}}^{P{(1)}}{\frac{1}{\rho}{P}}}} = {\int_{- 1}^{1}{A\; \rho \; u\; \frac{1}{2}u^{2}{x}}}}}$?indicates text missing or illegible when filed

The term ‘comprising’ as used in this specification and claims means‘consisting at least in part of’, that is to say when interpretingstatements in this specification and claims which include that term, thefeatures, prefaced by that term in each statement, all need to bepresent but other features can also be present. Related terms such as‘comprise’ and ‘comprised’ are to be interpreted in similar manner.

As used herein the term “and/or” means “and” or “or”, or both.

As used herein “(s)” following a noun means the plural and/or singularforms of the noun.

This invention may also be said broadly to consist in the parts,elements and features referred to or indicated in the specification ofthe application, individually or collectively, and any or allcombinations of any two or more of said parts, elements or features, andwhere specific integers are mentioned herein which have knownequivalents in the art to which this invention relates, such knownequivalents are deemed to be incorporated herein as if individually setforth.

In this description the following definitions are used:

A surface area

A_(entex) the surface area across which matter enters and exits thecontrol-volume

B,b exergy, specific exergy

C_(k) concentration of chemical species k

$\begin{Bmatrix}\gamma \\{\alpha \; \beta}\end{Bmatrix}\mspace{14mu} {Christoffel}\mspace{14mu} {Symbols}$

H, H_(ƒ,)h enthalpy, enthalpy of formation, specific enthalpy

{right arrow over (I)}_(k) diffusion vector of chemical species k

J_(j) rate of chemical reaction j

{right arrow over (m)} unit vector normal to the surface

P pressure

{dot over (Q)} magnitude of heat interaction per volume

S,s entropy, specific entropy

R^(i) general notation for intensive properties R^(i)=T, etc.

T absolute temperature

t time

u velocity in the x direction

V volume

{right arrow over (v)} velocity vector

{dot over (W)} the rate of shaft work output (shaft power output), ηthermal efficiency

p density

σ stress tensor

p_(k) density of species k

Ψ specific potential energy

μ chemical potential μ_(k) chemical potential of species k

BRIEF DESCRIPTION OF THE FIGURES

The present invention will now be described with reference to theaccompanying drawings in which:

FIG. 1 shows a preferred form technique for maximising thermalefficiency.

FIG. 2 shows one implementation of a technique for maximising thermalefficiency.

FIG. 3 shows a preferred form computing device.

FIG. 4 shows the results of a first experiment.

FIG. 5 shows the results of a second experiment.

DETAILED DESCRIPTION OF PREFERRED FORMS

Thermal efficiency of a power-plant is defined as

$\begin{matrix}{\eta = {\frac{\overset{.}{W}}{\overset{.}{H}} = {\frac{\overset{.}{W}}{{\overset{.}{H}}_{f} + {\overset{.}{H}}^{\prime}} = {\frac{\overset{.}{W}}{{{\overset{.}{m}}_{f}h_{f}} + {\overset{.}{H}}^{\prime}} = \frac{\overset{.}{W}}{{{\overset{.}{m}}_{f}{Cv}} + {\overset{.}{H}}^{\prime}}}}}} & (1)\end{matrix}$

where {dot over (W)} is the rate of shaft work output (shaft poweroutput), {dot over (H)}_(f) is the rate of fuel energy input, {dot over(H)}^(F) is the rate of other energy inputs, h_(j) is fuel specificenthalpy which is the same as fuel calorific value Cv, {dot over(m)}_(f) is fuel mass-flow rate; η is measured in %.

For turbine plants the inverse

${HRT} = \frac{1}{\eta}$

called heat-rate is used; the units of HRT are Kwh/Kj or Kj/Kj.

The techniques maximize η (minimize HRT) with respect to a set ofindependent measured parameters called Variables. The Variables areavailable to an operator or an engineer to manipulate subject tooperational, safety, and structural constraints. In addition to thesestructural constraints there are external constraints like theenvironment. The Variables are independent in the sense that one or morecan be varied without affecting the others. If the load {dot over (W)}and C_(v), {dot over (H)}^(F) are externally dictated, then {dot over(m)}_(f) is to be minimized; however, one can invert this to a dictated{dot over (H)}_(f), {dot over (H)}^(F) then {dot over (W)} is to bemaximised.

It is intended that the technology below apply to both scenarios

It is well known that max(η) is equivalent to min (T₀Δ{dot over (S)})where Δ{dot over (S)} is the total rate of entropy production, T₀ is thetemperature of the sink, normally the environment (atmosphere, ocean)and T₀Δ{dot over (S)} is total plant's exergy-loss. A given T₀ is anexample of an environmental constraint. The techniques below do notrequire that T₀ be fixed. Rather the related quantity of reversible workis used.

FIG. 1 shows a preferred form technique for maximising thermalefficiency. The system 100 operates iteratively. It takes as input thecurrent actual state 105 of a physical power plant 100. A dataacquisition system 115 obtains available measured data. Conventionalmass and energy balance calculations are carried out 120. The intentionis that substantially every meaningful cross-section of the mass flowrate, temperature, pressure and chemical composition are known. In thisway the current state of the plant is obtained from available measureddata. The actual state of the plant constitutes all relevantthermodynamic properties throughout the plant. It is fed to the Solver125 at the start of the first iteration. The initial control set orVariables 130 include temperatures, pressures and flows. These aretypically determined by the user, who decides what the variables shouldbe. The settings of each variable are subject to constraints 135. Theseconstraints 135 are sent to a minimizer 140 and then to Solver 125.

The Solver 125 outputs a numerical solution 145 at least partly from amathematical model 150. The Solver 125 is used to generate the value ofan objective function 155 which is then tested against a convergencecriterion by a convergence tester 160. The tester 160 determines whetherthe values of the objective function 155 at the (current) jth iterationare “sufficiently close” to its value at jth-1 iteration. If yes thenthe criterion is satisfied and the Algorithm displays the Variables'values that maximise the plant's efficiency. Otherwise these are fedback into the minimizer 140 which feeds the jth set of Variables intothe Solver 125. Solver 125 then feeds the jth numerical 145 solutioninto the objective function 155 and the process is repeated.

The final values of the Variables generated by the system 100 can alsobe fed to the plant's control system and so render the maximizing of ηfully automatic.

System 100 further includes a simulator 165. One can show that thenumerical solution given by the Solver 125 at any iteration, say thejth, corresponds to an actual state of the plant dictated by the jth setof the Variables. The Variables are the only plant parameters that canbe varied independently. Hence one can tabulate the plant's actualstates against all the combinations of Variables generated by theminimizer 140 (this is of course, a multi-dimensional table).Furthermore one can take the minimizer 140 out of the loop, and generatethe said table for any number of arbitrary combinations of theVariables. Either way, for any set of values of the Variables the tableyields the corresponding plant's actual state. Such a table is asimulator by conventional definition. It makes a prediction of the stateof the plant if one changes the value of the Variable(s).

A plant, no matter how complex, constitutes a finite number ofcontinuities separated by boundaries also know as discontinuities. Sucha system is called semi-continuous. In a power plant these continuitiesare flows of the working fluids governed by the laws of Fluid-Mechanics.The most fundamental of these are the balances of momentum, mass, energyentropy, and electrical charge. The last of these is irrelevant to thetechniques described below. These balances can be written both inintegral and differential forms. The differential balance equations formass and energy and momentum can always be written in a divergent formwhich renders them Conservation Laws. The name comes from the factbecause of the divergent the integral form of the said balance is avanishing surface integral. This can be put more simply as “what goes ingoes out.” Because of its importance to what follows consider forexample the general balance of momentum:

$\begin{matrix}{{\rho \; \frac{\overset{arrow}{v}}{t}} = {{\frac{{\partial\rho}\; \overset{arrow}{v}}{\partial t} + {\nabla{\cdot ( {p\; \overset{arrow}{v}\; \overset{arrow}{v}} )}}} = {{\nabla{\cdot \overset{\overset{arrow}{\_}}{\sigma}}} - {\sum{{\overset{arrow}{F}}_{k} \cdot {\overset{arrow}{j}}_{k}}}}}} & (2)\end{matrix}$

The above mentioned system of partial differential equations (PDEs) isundetermined. Constituent (or phenomenological) equations complementthese PDEs. The fundamental constitutent coefficients and the symmetriesthey obey are already known. The numerical values of thephenomenological coefficients are not normally known; for the mostimportant ones there are tabulated empirical values which are by nomeans standards. Whichever the method, the assumption that thephenomenological coefficients even exist, is enabled by a balance ofentropy equation which is not a conservation law.

Balance of entropy can be reduced to a conservation law only forreversible flows. For such a fluid the rate of entropy production iszero, ie it satisfies:

$\begin{matrix}{{{{\nabla( \frac{1}{T} )} \cdot \overset{arrow}{Q}} = 0},{{\frac{1}{T^{\overset{\overset{arrow}{\_}}{\tau}}}:{\nabla\overset{arrow}{v}}} = 0},{{\sum\limits_{h}{( {\frac{F_{k}}{T} - {\nabla\; \frac{\mu_{k}}{T}}} ) \cdot {\overset{arrow}{j}}_{k}}} = 0}} & (3)\end{matrix}$

For a reversible fluid the phenomenological coefficients all vanish. Afluid for which σ=0 is known as a perfect fluid. For a perfect fluid thebalance of momentum equation reduces to Euler's equation of motion. Itis well known that even under the assumption of perfect fluid the set ofEuler's equations and conservation of mass are underdetermined in the 3components of the velocity field, pressure field, and density field.Hence for various applications some other assumptions are added towell-pose the system of PDEs. The best known are isentropic orisothermal flow, or some truncated equation of state. The term p=p(P) isone of the most commonly used.

Referring to FIG. 1 the mathematical model 150 comprises Euler'sequation, conservation of mass and either the equation of ThermodynamicGeodesic Field (TGF) in the thermodynamic metric, or a direct ReversibleEnergy Conservation (REC) equation. This mathematical model accuratelyrepresents a reversible flow. Either TGF or REC can be used. The twoequations TGF and REC are equivalent for the techniques described here.Other equations which are best described as different flavours of REC orTGF can also be used. The numerical solution of the mathematical model150 is an accurate state of a reversible equivalent of the actual plant.The power output of the reversible equivalent is the maximum possible,subject to the given thermodynamic boundary conditions of the plant. Theactual power is dictated as a constraint. The intention is to minimizethe reversible power by manipulating the Variables, because the loss issimply the reversible power minus the actual power.

The simulator 165 tabulates the numerical outputs of the Solver 125 fordifferent sets of Variables. These tables correspond to predictions ofthe state of the actual plant. This is surprising, since the many modelsof continuous fluid-flow all call upon Navier-Stokes equations (also abalance of momentum), which depend upon 2 empirical phenomenologicalcoefficients, and the solving of which involves further ad-hocassumptions. These equations are heavy on computer resources, may noteven be solvable, or are very difficult to integrate for an entireplant, which is the main reason why there is no efficiency maximize fora power plant at present.

The techniques also claim to accurately predict actual parameters of thecontinuum through the mathematical model of the reversible flow, butonly at the terminals (i.e. at Aent, Aex) of the continuum. This is theprice paid for the simplification. However these are the only ones whereproperties are measurable by power-plant engineers.

Consider a steam-turbine as a subprocess of a power plant. It can bedescribed as a single continuum. The ordered pairwhich is the Clausiusnotion of a process, are the states on steam entering and existingcross-sections (Aentex) of the turbine.

The maximum possible magnitude of work interaction subject to the givenend states is delivered by a reversible process which can be anisentropic turbine, diverting part of its power to drive a Carnotheat-pump, which in turn maintains the Aentex (end) states of the actualturbine by drawing heat from reservoirs (the environment).

The total rate of entropy production of the isentropic turbine, theCarnot heat-pump and reservoirs is zero; hence the process isreversible. In other words the actual turbine is replaced by anisentropic one plus a Carnot heat-pump which is compensated to maintainthe Aent, Aex thermodynamic states.

These techniques apply the said principle to a continuum. The generalstatement is that for every given (irreversible) continuum there existsa reversible continuum which delivers maximum work, such that values ofthe thermodynamic properties at the boundary of the original continuumare maintained. Such a substitution of a reversible continuum for anactual irreversible continuum is referred to here as Reversible Masking.

These techniques establish that the converse is also true, that is, onecan recover the original continuum from the reversible one. It is theinversion from predicted reversible to predicted actual, which enablesthe function of simulator 165.

Mathematical model 150 does not require any prior knowledge of plant'sdimensions, or any other (plant component's) characteristics, or anyempirical tabulated data save thermodynamic properties h,s,v, of theworking fluids. The model is also free of ad-hoc assumption, hence itsaccuracy. The same mathematical model can be used as a stand-alone topredict variations of the plant parameters other than maximum work, bothfor dynamics and steady-state.

The model has the potential to be fast, light on computer resources, anduniversal. The key to the success of the mathematical model lies with anaugmentation to Euler's balance-of-momentum equations as presentedbelow.

This augmentation is an energy conservation equation for a reversibleprocess (REC) without reference to external systems like theenvironment. The techniques described below include a number of suchaugmenting equations, all equivalent.

The full, well-posed system of PDEs is set out below. For a reversibleflow the shear stress components τ_(ij) are zero hence equation (2)reduces to the Euler equation.

$\begin{matrix}{{\rho \frac{\partial\overset{arrow}{v}}{\partial t}} = {{\frac{\partial( {\rho \overset{arrow}{v}} )}{\partial t} + {{\rho ( {\overset{arrow}{v} \cdot \nabla} )}\overset{arrow}{v}}} = {{- {\nabla P}} - {\Sigma {{\overset{arrow}{F}}_{k} \cdot {\overset{arrow}{j}}_{k}}}}}} & (4)\end{matrix}$

Conservation of mass of a continuum subject to a variable cross sectionarea

$\begin{matrix}{{\frac{\partial( {A\; \rho_{k}} )}{\partial t} + {\nabla{\cdot \lbrack {A( {{\overset{arrow}{j}}_{k} + {\rho_{k}\overset{arrow}{v}}} )} \rbrack}}} = {\frac{\partial}{\partial t}\lbrack {A \times M_{k}{\sum\limits_{j = 1}^{r}\; {v_{kj}( {\rho {\overset{\sim}{n}}_{j}} )}}} \rbrack}} & (5)\end{matrix}$

In the above equation:

M_(k) is the mass of species k,

{right arrow over (I)}_(k)=p_(k){right arrow over (v)} is the diffusionflux of species k, and ñ_(j) is the number of Kmoles of chemicalreaction j per Kg of total mass.

The rate of chemical reaction j is

$J_{j} = {\frac{\partial( {\rho {\overset{\sim}{n}}_{j}} )}{\partial t}.}$

Conservation of energy for a reversible flow (REC) equation.

$\begin{matrix}{{{\frac{\partial}{\partial t}( {{\rho \; \frac{1}{2}{\overset{arrow}{v}}^{2}} + \psi} )} + {\nabla{\cdot ( {{\rho \; \frac{1}{2}{\overset{arrow}{v}}^{2}} + \psi} )}} + ( {{\sum\limits_{j = 1}^{R}{\sum\limits_{k = 1}^{K}{\mu_{k}v_{kj}J_{j}}}} - {\rho \; \overset{.}{Q}}} )} = {- ( {{\sum{\mu_{k}\frac{{\partial\rho}\; c_{k}}{\partial t}}} + {{\nabla{\cdot {\rho ( {h - T_{0}} )}}}\overset{arrow}{v}} - {\nabla{\cdot {\sum{\mu_{k}{\overset{arrow}{j}}_{k}}}}}} )}} & (6)\end{matrix}$

In addition there are the thermodynamic equations of state

p=p(P,T,c _(k)),h−Ts=g=g(P,T,c _(k)), μ_(k)=μ_(k)(P,T,c _(k)), k=1 . . .N

For the system to be well-posed the number of unknown functions mustequal the number of differential equations. The unknown functions arethe 3 components of the velocity {right arrow over (v)}, the density p,the Gibbs function g, the pressure P, the temperature T, altogether 7unknowns. Plus the N densities p_(k), the N chemical potentials μ_(k),altogether 2N+7 unknowns. There are 3 Euler conservation of momentumequations, 1 equation of reversible conservation of energy, N equationsof conservation of mass, N equations of state μ_(k)=μ_(k)(P,T,p), 2equations of state

${g = {g( {P,T,\rho_{j}} )}},{\rho = {\rho ( {P,T,\rho_{j}} )}},{{{and}\mspace{20mu} \rho} = {{{\sum\limits_{k}\; {{\rho_{k}.{Altogether}}\mspace{14mu} 3}} + 1 + {2\; N} + 2 + 1} = {{2\; N} + 7.}}}$

Discussion is initially limited to 2 spatial dimensions x,y and time t(2 d+1), that is, the unknown functions do not vary in the direction.Given the distribution of the cross-sectional area A(x,y,t), and theinitial (at time t=t₀) values of the unknown functions on a regionf(x(t₀),y(t₀),t₀)=0 on the spatial x-y plane, then the set of equations(4) to (6) is well posed and can be solved yielding the spatialdistribution of the unknown functions at any time t i.e. the values of{right arrow over (v)}(x,y,t),P(x,y,t),T(x,y,t),p_(k)(x,y,t),μ_(k)(x,y,t), p(x,y,t), g(x,y,t) for all x,y,t varying betweenpredetermined limits. The cross-sectional area A is such that thespatial vector {right arrow over (n)} normal to A lies on the spatialx,y,t∀x,y, t plane. In other words the A intersects the x-y plane alonga curve that can be of any shape. If the said intersecting curve is astraight line perpendicular to the x axis everywhere, then the flow is 1d+1. This is known as cylindrically symmetric.

Alternatively, one can replace the 3 equations of the conservation ofmomentum (Euler) by the geodesic equations (TGF) in the spatialcoordinates (the summation convention applies)

$\begin{matrix}{{{\frac{\partial v^{\gamma}}{\partial q^{S}}v^{S}} + {\begin{Bmatrix}\gamma \\{a,s}\end{Bmatrix}v^{\alpha}v^{\beta}}} = 0} & (7)\end{matrix}$

where the q coordinates are in the Galilean 2+1 space, and theChristoffel Symbols are in an induced metric. This induced metric isdescribed in Weinhold F. 1975 Metric Geometry of EquilibriumThermodynamics (followed by II,III,IV,V) Journal of Chemical Physics 63:2479-2483. It is referred to as the Weinhold metric. This metric is notcommonly known hence it is rather preferable to replace the N equationsof conservation of mass plus the equation of reversible conservation ofenergy plus the equation of state g=g(P,T,c_(k)) by N+2 geodesicsequations in the thermodynamic coordinates, in this case P,T,p_(k), herethe Christoffel Symbols are in the Weinhold metric which can be derivedfrom standard thermodynamic properties functions and the knowledge ofthe chemical reaction

$\begin{matrix}{{{{\frac{\partial{\overset{.}{R}}^{k}}{\partial R^{j}}{\overset{.}{R}}^{j}} + {\begin{Bmatrix}k \\{ij}\end{Bmatrix}{\overset{.}{R}}^{i}{\overset{.}{R}}^{j}}} = 0};{\frac{R^{k}}{t} = {\overset{.}{R}}^{k}}} & (8)\end{matrix}$

Strictly speaking equations (4,5,6,8) are (2N+2)×2 equations with theadditional 2N+2 variables {dot over (H)}^(k).

Equation (8) is equivalent to the 2^(nd) order system in the parametert.

$\begin{matrix}{{{\frac{^{2}R^{1}}{t^{2}} + {\begin{Bmatrix}i \\{jk}\end{Bmatrix}\frac{R^{j}}{t}\frac{R^{k}}{t}}} = 0}{{R^{1} = T},{R^{2} = P},{R^{3} = {\rho (1)}},{R^{4} = {{{\rho (2)}\mspace{14mu} \ldots \mspace{14mu} R^{N + 2}} = {\rho (N)}}}}{{{R^{1}( {t = 0} )} = R_{0}^{1}},{{R^{1}( {t = t_{2}} )} = R_{2}^{4}},{\rho_{2} = {\rho ( {T,{T(P)}} )}}}} & (9)\end{matrix}$

Clearly equation (8) is an augmentation to Euler's equations replacingboth energy and mass conservation equations. The solutions are in factthe same. The left hand side structure of both equations is the samei.e. the covariant derivative of the velocity {right arrow over (v)},however in different metrics. Even though the right hand sides differthe solution is still the same. Either way, the solution is valid onlyfor reversible flows. Described below is how this applies to realirreversible flows.

A plant is commissioned with measuring instruments such that it ispossible to compute all stationary-state relevant mass-flow-rates byintegral energy and mass balances alone. This is so because theefficiency monitoring is most important for stationary-state which iswhere a power plant normally is. To minimize the cost ofinstrumentation, manufacturers arrange measuring instruments across thepower plant such that the basic continuums assume cylindrical symmetry,hence are in effect one-dimensional. For example there is normally onethermometer at a turbine inlet main stream pipe and one at its exhaust,implicitly assuming that this single theremometer(s) represent thecross-sectional temperature distribution.

If the actual continuum is in one-dimensional stationary-state then sois its Reversible Masking, that is, all

$\frac{\partial}{\partial t}$

of equations (4) to (6) vanish, and velocities and other properties varyonly in the x-direction. Hence the reversible conservation PDEs can bereduced to ODEs, or even be reduced further to algebraic equations. Thetime independent 1 d balance of momentum

$\begin{matrix}{\frac{\partial( {\rho \; {uu}} )}{\partial x} = { {{- \frac{\partial P}{\partial x}} - {\Sigma {{\overset{arrow}{F}}_{k} \cdot {\overset{arrow}{J}}_{k}}}}\Rightarrow{u\frac{\partial u}{\partial x}}  = {{{- \rho^{- 1}}\frac{\partial P}{\partial x}} - {\Sigma {{\overset{arrow}{F}}_{k} \cdot {\overset{arrow}{j}}_{k}}}}}} & (10)\end{matrix}$

For 1 d stationary-state it is more convenient to work with the“diffuser-nozzle theory”

$\begin{matrix}{\frac{dA}{A} = {{\frac{dP}{\rho \; u^{2}} - \frac{d\; \rho}{\rho}} = {{\frac{dP}{\rho \; u^{2}}( {1 - {u^{2}\frac{\partial\rho}{\partial P}}} )} = {\frac{dP}{\rho \; u^{2}}( {1 - {Ma}^{2}} )}}}} & (11)\end{matrix}$

where Ma is the Mach number. Writing this in one-dimension in thedirection of x

$\begin{matrix}{{\frac{1}{A}\frac{A}{x}} = {{\frac{1}{\rho \; u^{2}}\frac{P}{x}( {1 - {u^{2}\frac{\partial\rho}{\partial P}}} )} = {\frac{1}{\rho \; u^{2}}\frac{P}{{x( {1 - {Ma}^{2}} )}}}}} & (12)\end{matrix}$

Equations (11, 12) are a resultant of combining momentum and continuity,hence one can use equation (12) instead of Euler's equation.

The conservation of mass equation (5) in 1 d, is

$\begin{matrix}{{\frac{\partial( {A\; \rho \overset{arrow}{v}} )}{\partial t} + {\nabla{\cdot {A( {{\rho \overset{arrow}{v}} + {\overset{arrow}{j}}_{k}} )}}}} = {{\frac{\partial( {A\; \rho_{k}u} )}{\partial t} + \frac{\partial( {{A\; \rho_{k}u} + j_{k}} )}{\partial x}} = {\frac{\partial}{\partial t}\lbrack {A \times M_{k}{\sum\limits_{j = 1}^{r}\; {v_{kj}( {\rho {\overset{\sim}{n}}_{j}} )}}} \rbrack}}} & (13)\end{matrix}$

With chemical reaction but otherwise stationary state this reduces to

$\begin{matrix}{\frac{\partial( {{A\; \rho_{k}u} + j_{k}} )}{\partial x} = {\frac{\partial}{\partial t}\lbrack {A \times M_{k}{\sum\limits_{j = 1}^{r}\; {v_{kj}( {\rho {\overset{\sim}{n}}_{j}} )}}} \rbrack}} & (14)\end{matrix}$

Conservation of energy for a reversible flow (REC) (6) for ldstationary-state with chemical reaction is

$\begin{matrix}{{{\frac{\partial}{\partial x}( {{\rho \frac{1}{2}u^{2}} + \phi} )} + ( {{\sum\limits_{j = 1}^{R}\; {\sum\limits_{k = 1}^{K}\; {\mu_{k}v_{kj}J_{j}}}} - {\rho \; \overset{.}{Q}}} )} = {- \lbrack {\frac{\partial}{\partial x}( {{{\rho ( {h - {Ts}} )}u} - {{\Sigma\mu}_{k}j_{k}}} )} \rbrack}} & (15)\end{matrix}$

The geodesic equations (8,9) remain unchanged because they are in thethermodynamic space. Spatial coordinates are not normally known for agiven plant. However for performance calculation these are irrelevant.One normalizes to an interval (−1;1). To solve the N+3 first order ODEs(12, 14, 15) and N Equations-of State in the 2N+3 functions

P(x),T(x),g(x),p(x),p_(k)(x),μ_(k)(x), u(x).

To solve these equations, one needs to know the cross sectional areaA(x) for the reversible continuum. This is obtained by combining thesystem (12,14,15) and the N Equations-of-State together with theintegral energy and mass balances of the actual (real, irreversible)continuum e.g. {dot over (M)}Δh={dot over (W)}+{dot over (Q)}.

A delicate but important point to note here, is, that necessarily themass-flow-rate is common to both the Masked (reversible) and actualcontinuum. The extra magnitude of work interaction manifests itself asdifferences in velocities only. Hence {dot over(M)}=[Apu]_(Aent)=[Apu]_(Aexer), {dot over (W)}, {dot over (Q)} are theactual magnitudes of work and heat interactions (load). Δh are the givenenthalpies difference at Aentex of the plant's continuums. Theadditional actual energy balance equation combines with (12,14,15) andEquations-of-State is well-posed in the 2N+3 unknown functions plusA(x), which is then kept fixed through the iterations following the loopshown in FIG. 1.

By varying the initial conditions at Aent (x=−1) for first order ODEs(12,14,15) P(x₀), T(x₀), g(x₀),p(x₀), μ_(k)(x₀), one obtains new valuesfor the functions P(x),T(x),g(x),p(x),p_(k)(x),μ_(k)(x), as well as foru(x). In particular one obtains the values at Aex(x=1). Thesepredictions are the essence of the mathematical model of a reversiblecontinuum in 1 d.

It follows therefore, that the state of the entire Masked (reversible)plant is determined by the values of the free Variables. These decidethe initial conditions of the plant's terminal continuums Aent.

Solving the mathematical model for terminal continuums gives the stateat their Aex, which, in turn, is the state of the next cascadingcontinuum and so on until the functions ofP(x),T(x),g(x),p(x),p_(k)(x),μ_(k)(x)u(x), are known for all continuumsthat make up the plant. That is, the state of the entire Masked(reversible) plant is deduced. If it so happens that one or morecontinuums are not included in the cascade, then either there are morefree variables, or the excluded set of continuums is indifferent to theVariables.

It follows, that varying the free Variables yields a new state of thereversible plant, as one would expect from a mathematical model. Eachiteration around the loop shown in FIG. 1 generates a new state of thereversible plant which yields a new value of maximum work—the objectivefunction to be minimized.

The objective of maximizing is equivalent to minimizing the sum of allplant's exergy-losses. These techniques focus on the more primitiveconcept of Maximum Work or maximum power. The very definition of lossesis the Lost Work, i.e. the difference between the maximum power, (whichcorresponds to the rate of work delivered in a reversible plant), andthe actual electrical power output. Since the latter is predetermined,then minimizing the Reversible Work will minimize the losses.

The maximum rate of work delivered by the Masked (reversible) continuum,i.e. its Reversible

Work, is the difference in kinetic energy at its Aent, Aex. That is

$\begin{matrix}{{\text{?} = {{\Sigma {\int_{P{({- 1})}}^{P{(1)}}{\frac{1}{\rho}\ {P}}}} = {\int_{- 1}^{1}{{Apu}\frac{1}{2}u^{2}\ {x}}}}}{\text{?}\text{indicates text missing or illegible when filed}}} & (16)\end{matrix}$

where the summing up is over all continuums; the summation yields thereversible work of the entire plant. It is this sum which is theobjective function to be minimized, which for given electrical load willminimize the plant's fuel flow-rate subject to the operational andenvironmental constraints.

The techniques and systems described above comprise 2 main parts:

-   -   1. The objective function to be minimized which is the rate of        kinetic energy delivered by a reversible representation of the        actual plant. This minimization is equivalent to minimization of        thermodynamic losses.    -   2. An accurate mathematical model that accurately determines how        variations in losses in one or more part(s) of the plant affect        the rest of it. Such variations can, in turn, be caused by        manipulating the Variables. The accuracy of the model is        facilitated by the Reversible Energy Conservation equation or        the Thermodynamic Geodesic Field equation, augmenting Euler's        equations. It is in essence a mathematical model of the        reversible plant which assumes the same thermodynamic values at        each cross-section as the actual plant.

The accuracy of the mathematical model combined with the built-inconstraints guarantees that the system-generated values for the7₁-maximising Variables are in fact attainable in practice.

The mathematical model can in fact simulate a real plant even though theequations as such correspond to a reversible process. There is no needfor ad-hoc assumptions and empirically derived tabulated data other thanthermodynamic properties of working fluids. The model is fast, light oncomputer resources, and universal.

FIG. 2 shows at 200 one example of implementation of the techniquesdescribed above. Power plant 205 includes any one or more of a steamturbine, combined cycle, cogeneration power plant, diesel cycle, andnuclear.

Plant 205 has associated with it a plant archive 210. This plant archiveis maintained in computer memory or secondary storage. The plant archivecomprises time stamped efficiency data for some or all components ofplant 205. The plant archive 210 is used to determine the current plantstate.

A server configuration 215 carries out the functions described aboveperformed by the solver 125 of FIG. 1. The server configuration 215includes for example at least one display device, a processor, computermemory, and computer network components.

The results of analysing efficiencies can be displayed on displaydevices associated with the server configuration 215. The results canalso be transmitted over a data network 220 to one or more clientprocessing devices 225 operated by an operator. The results can bedisplayed on display devices associated with client device 225. The datacan also be produced in hard copy on an associated printer device orsaved in a data file on associated secondary storage.

A further embodiment of the system 200 transmits data from plant archive210 to server configuration 215. The server 215 then automaticallyadjusts parameters of the plant 205 based on convergence calculations ithas determined.

FIG. 3 shows a simplified block diagram of a machine in the example formof a computing device 300. The server configuration 215 is one exampleof computing device 300. In one embodiment the server configuration 215operates as a standalone computing device with network connectionsallowing it to access current values of client instrumentation. Theserver configuration 215 reports recommendations on both the deviceitself and via a network to other clients. In an alternative embodimentthe techniques described above are executed entirely within a controlsystem computing device associated with the plant 205.

Sets of computer executable instructions are executed within device 300that cause the device 300 to perform the methods described above.Preferably the computing device 300 is connected to other devices. Wherethe device is networked to other devices, the device is configured tooperate in the capacity of a server or a client machine in aserver-client network environment. Alternatively the device can operateas a peer machine in a peer-to-peer or distributed network environment.The device may also include any other machine capable of executing a setof instructions that specify actions to be taken by that machine. Theseinstructions can be sequential or otherwise.

A single device 300 is shown in FIG. 3. The term “computing device” alsoincludes any collection of machines that individually or jointly executea set or multiple sets of instructions to perform any one or more of themethods described above.

The example computing device 300 includes a processor 302. One exampleof a processor is a central processing unit or CPU. The device furtherincludes main system memory 304 and static memory 306. The processor302, main memory 304 and static memory 306 communicate with each othervia data bus 308.

Computing device 300 further includes a data input device 310. In oneembodiment the data input device includes a computer keyboard. Thedevice 310 includes both a physical keyboard and/or a representation ofa keyboard displayed on a touch sensitive display for example displaydevice 312.

Computing device 300 may also include reader unit 314, network interfacedevice 316, display device 312, optical media drive 318, cursor controldevice 320, and signal generation device 322.

Reader unit 314 is able to receive a machine readable medium 324 onwhich is stored one or more sets of instructions and data structures,for example computer software 326. The software 326 uses one or more ofthe methods or functions described above. Reader unit 314 includes adisc drive and/or a USB port. In these cases the machine readable mediumincludes a floppy disc and a static storage device such as a thumbdrive. Where the optical media drive 318 is used, the machine readablemedium includes a CD Rom.

Software 326 may also reside completely or at least partially withinmain system memory 304 and/or within processor 302 during execution bythe computing device 300. In this case main memory 304 and processor 302constitute machine-readable tangible storage media. Software 326 mayfurther be transmitted or received over network 328 via networkinterface device 316. The data transfer uses any one of a number of wellknown transfer protocols. Once example is hypertext transfer protocol(http).

Machine-readable medium 324 is shown in an example embodiment to be asingle medium. This term should however be taken to include a singlemedium or multiple media. Examples of multiple media include acentralised or distributed database and/or associated caches. Thesemultiple media store the one or more sets of computer executableinstructions. The term “machine readable medium” should also be taken toinclude any medium that is capable of storing, encoding or carrying aset of instructions for execution by the machine and that cause themachine to perform any one or more of the methods described above. Themachine-readable medium is also capable of storing, encoding or carryingdata structures used by or associated with these sets of instructions.The term “machine-readable medium” includes solid-state memories,optical media, magnetic media and carrier wave signals.

In one embodiment the software is installed and operating at a clientsite on a computing device 300. Network interface device 316 is requiredto communicate with an offsite central server for example to submit dataresults and licence validations.

In some cases the network interface device 316 and network 328 are notrequired as the system can run in a stand alone mode. This means that nodata results are submitted to the offsite central server.

The techniques described above have been tested on a power station innormal operating conditions. While the power plant was running at aconstant power output, the instrument data was analysed by the inventionand new recommendations for operating parameters measurementscalculated. The plant operators then adjusted the plant parameters tothese recommendations and efficiency was observed to improve.

FIG. 4 shows a first experiment run at a Huntly power station on 7 Dec.2007 from 13:30 to 21:00.

The system described above recommended changes which required anoperator to change attemperator flow-rates, main steam temperature,reheater temperature, and burner angle of tilting. Operator interventionbegan around 15:50. The heat rate was observed to improve or drop byclose to 2%.

FIG. 5 shows a second experiment that was run at the Huntly powerstation from 16 May 2008 starting at 18:00 to 17 May 2008 at 04:00.

The techniques described above recommended another combination ofattemperator flow-rates, main steam and reheater temperature and theburner tilt angle.

Operator intervention commenced at 22:00 and heat-rate improvements of1.5 to 2% were observed.

The techniques described above result in changes made to thermalefficiency of a power plant. In one embodiment the results of theequations above are applied manually to the plant by a user such as aplant operator. This is known as an open loop application. Alternativelythe changes to the plant are applied automatically by a control systemassociated with the plant. This is known as a closed loop system.

The foregoing describes the invention including preferred forms thereof.Modifications and improvements as would be obvious to those skilled inthe art are intended to be incorporated in the scope hereof, as definedby the accompanying claims.

1. A computer implemented method of controlling any energy conversionplant, in particular power plants of all kinds, having a plurality ofmeasured parameters (which may include temperatures, pressures, partialpressures, mole numbers, as well as flows ,in and out electrical and/ormechanical powers, position of valves, and other actuators), thatmaximizes the plant's thermal efficiency with respect to a subset of theplant's measured parameters which can be manipulated, hence termedVariables, subject to operational structural financial and environmentalconstraints; this constrained maximization is called optimizing; saidcomputer is either integral part of the plant's control system (DCS orother) in the sense that it both reads measured parameter from the DCS'sData Acquisition System (DAS) and writes the Variables maximizing valuesinto the DSC as set-points (closed loop optimization), or just readsmeasured parameter from the DAS whilst human operators apply maximizingvalue of the Variables as set-points or by modifying the plant itself(open loop optimization), said method constitutes the following steps:(a) Determine set of all relevant measured thermodynamic propertiesthroughout the plant (e.g. temperatures, pressures, partial pressures,mole number, liquid and gas flows and electrical input and output valuesposition of valves and other actuators), and its Variables subset (thatis, those measured parameters which can be independently manipulated),by reading them via an interface with the DAS, or manual input, (b)derive from the measured parameters in accordance to step (1a) andcorresponding thermodynamic properties (e.g. specific volume enthalpyand entropy), the state of the plant which constitutes all relevantthermodynamic properties throughout the plant, as well as energy massand entropy flows, temperatures, pressures, partial pressures, molenumbers, liquid and gas flows and electrical input and output values,real velocity vector fields, by way of relevant balance equations andparticular expressions; (c) from the plant state determined in step (1b)partition the plant into a finite number of real, irreversible physicalcontinuums in the context of continuum-mechanics, which may or may notdeliver useful work, and which correspond to discontinuities of measuredand derived parameters making up the state of the plant as establishedin step (1b), and satisfying conservation-of-mass condition(s), (d)construct an isometric (in the thermodynamic metric) map in the contextof differential geometry, of each real continuum as established in step(1c) from the thermodynamic manifold which is spanned by thermodynamiccoordinates (for example pressure temperature and chemical potentials)and time, to a region of the Galilean manifold spanned by the spatialand time coordinates (for example Cartesian x,y,z,t), (e) construct theplant model using the partition into physical continuums determined inaccordance to step (1c) and in accordance of the physical realarrangement of the plant's actual hardware, as interfacing (i.e.incedenting) physical continuums, exhibited as a graph in the context ofgraph theory which can be reduced to a planar graph, wherein eachboundary plays the role of an edge and each continuum the role of anode, (f) convert each partitioned real, irreversible physical continuuminto a (virtual) corresponding reversible continuum or ReversibleMasking of the real continuum, subject to the constraint(s) that thereal continuum and reversible continuum assume the same boundary valuesof thermodynamic properties in accordance to all previous steps and thattheir derivatives are continuous and equal at the boundaries, as well asmass-flow-rate, such that the partitioned irreversible real continuumswhich are governed by a system of conventional balance equations andconstituent (phenomenological) equations, are converted into partitionedReversible Maskings substitute which are governed by a system of(partial) differential equations excluding any constituent equations,but including either the equation of Thermodynamic Geodesic Field (TGF)in the thermodynamic metric, or a direct Reversible Energy Conservation(REC), uniquely describing the reversible continuum (called aMathematical Model of the reversible continuum), (g) construct anequivalent reversible (virtual) plant by mapping the partitionedReversible Masking substitute equations from step (1f) into the plantmodel constructed in step (1e), such that the graph of step (1e) ismaintained, that is, map the partition of the real plant of irreversiblereal continuums, into a partition of Reversible Maskings substituteequations, with the same incidence matrix in the context of graphtheory, (h) solve the mapped equations from step (1g) for the currentplant state in terms of velocity (vector) fields across the reversiblecontinuums and store the values of the solutions within the spacesdefined by the reversible continuums, (i) construct the objectivefunction (called Loss) to be minimized by a surface integral of kineticenergy obtained from the velocity field derived according to step (1h)over the boundary of each Reversible Masking, inputting to the(numerical) integration the velocity field, density field(s) of (1e)values at the boundary, outputting the difference in kinetic energybetween boundaries where matter leaves and enters the ReversibleMasking, subtracting from the sum of all kinetic energy increment theactual work delivered by the real plant, (j) simulate the plant usingthe solved equations from step (1g) using the reversible model andadjust the control set-points in the simulation to determine theVariables (control inputs) defined in 1 that correspond to theminimization of the Loss constructed in step (1i) resulting inmaximizing the efficiency of the plant according to a predeterminedobjective function, (k) apply the Variables (control inputs) derivedaccording to step (1j) that minimize the objective function constructedaccording to step (1i) to the real thermal power plant.
 2. A method togenerate a revised state of the plant and reversible velocity fields dueto varying the Variables subset defined in claim 1), based at leastpartly on a (power) plant configuration in accordance to step (le),superimposed by the Reversible Masking in accordance to step (1f), andconsequent reversible plant in accordance to step (1g) comprising asolver as follows: (a) Euler's balance of momentum equation; and (b) theconservation of mass equation; and (c) the reversible conservation ofenergy (REC) equation; and (d) the thermodynamic equations of state; or(e) the thermodynamic geodesic field (TGF) equations, (f) and a moduleto carry out the numerical solution of the simultaneous equations (2a)to (2e) subject to revised boundary conditions based at least partly onCentral Schemes methods, Method of Lines, or reduced versions thereof.3. A simulator constituting a readable media module storing the datathat flows from the numerical solution module defined in (2f) whichsimulates the thermodynamic properties of the real plant.
 4. A method toderive kinetic energy differences across each of the reversiblecontinuums defined in step (1f), from the data flow of the reversiblevelocity field(s) computed by the solver defined in claim 2), which isfed into a module of numerical integration of kinetic energy around thesurface of each reversible continuum.
 5. A method to obtain theobjective function constituting the sum of all kinetic energy integrals,of all Reversible Maskings defined in step (1f).
 6. An apparatus for anyone of the preceding claims herein comprising a (power) plant thermalefficiency constrained-maximization (optimization), the apparatusconfigured to implement the method of claim 1, that is, configured toobtain the current state of the plant from available measured data;obtain the Variables subset of the measured data defined in claim 1;apply a set of constraints to the Variables; generate a revised state ofthe reversible power plant, where the reversible plant is defined instep (1g), as a function of the revised set of Variables, the generationbased at least partly on mathematical model of the reversible continuum(or Reversible Masking) of step (1f);and test the revised set ofVariables for convergence, comprising the following modules and dataflows: (a) interfacing module with the DAS or exercising manual input inaccordance with claim 1), to determine initial values of the set of allrelevant measured thermodynamic properties throughout the plant inaccordance to step (1a); the measured data and the Variables subset flowto readable media modules; (b) a module that generates the initial(current) state of the plant as defined in step (1b), from the measuredparameters in accordance to step (1a) which is stored in a moduledepicted in (6a) and the corresponding thermodynamic properties (e.g.specific volume, enthalpy and entropy), (c) a module constructing thepartition into physical continuums in accordance to step (1c), based atleast partly on checking each combination of boundary-surfaces ofmass-flow entering the continuum against all combinations ofboundary-surfaces of mass-flow leaving the continuum for conservation ofmass; as a result each continuum is reduced to cylindrical symmetry(1-dimensional), and furthermore the plant is exhibited as a planargraph in the context of graph theory, wherein each boundary ofinterfacing (i.e. incedenting) physical continuum plays the role of anedge, and each continuum the role of a node, and furthermore theresultant plant model is as defined in step (1e), (d) a convergencetester module which can be part of the minimizer procedure (likeCobyla), within which the solver of claim 2), the simulator of claim 3),and the objective function in accordance to claim 5), are applied inthat order to the plant model of module (6c) and the revised set ofVariables, which is then examined to reach a variance less than athreshold variance; if the convergence test fails, then the revisednumerical values of the objective function and the Variables and stateof the plant which are stored in the simulator module of claim 3) above,are fed into (e) a minimizer module like Cobyla which generates revisedvalues of the set of Variables defined in claim 1) which are fed intothe mathematical model of the reversible plant (that is the solver ofclaim 2)), and (f) repeating convergence testing described in (6d) ofgenerating yet another revised state of the plant and reversiblevelocity field, and testing the resultant revised objective function asdefined in step (1i) and generated in accordance to claim 5), andtesting the revised set of Variables for a variance less than athreshold variance in the convergence tester module (6d); if achieved,then (g) physically applying continuously the Variables values generatedin module (6f) which is the Optimizer output, to the (real) energyconversion plant, by way of closed loop optimization or open loopoptimization in accordance with claim 1), necessarily resulting inminimizing the objective function (Losses) defined in step (1i), andgenerated in accordance to (6d), resulting in the maximizing of thethermal efficiency of the real plant; if a constraint in the context ofclaim 1) is a given power output then said maximizing of thermalefficiency will manifest itself as the minimizing of fuel consumption,whilst if the fuel consumption is rather dictated as an externalconstraint, then said maximizing of thermal efficiency will manifestitself as the maximizing of power output.